That's a great question. In my opinion, in the case of neurology, both the nature of neuroscience research and of neurological diseases are factors. Neuroscience research is very much physics-based and requires a lot of technology- which obviously wasn't available in the past. In the 1990's (The "Decade of the Brain") there was an explosion in neuroscience research as technology improved. Furthermore, neurological diseases are chronic (for the most part) and have become more common as the average lifespan has increased. I would imagine that more research funding is directed to curing more deadly diseases, whereas less is directed to curing conditions that mostly affect quality of life. However, I think that this is changing to some degree. NIH provides about equal funding for "cancer" and "brain disorders."
In the case of psychiatry/psychology, research and progress has may have been limited due to the lack of technology as well as the presence of competing philosophies or "schools of thought" such as behaviorism.
I highly recommend that you read work by Vilayanur S. Ramachandran (MD, PhD). He does some amazing research in cognitive neuroscience in areas like phantom limb sensation, synesthesia. He has a lot of interesting theories on some of the most important questions regarding human nature- Do we have a soul? Is there a god part of the brain? etc.